Tangen

Tangen (lambang tg, tan; bahasa Belanda: tangens; bahasa Inggris: tangent) dalam matematika adalah perbandingan sisi segitiga yang ada di depan sudut dengan sisi segitiga yang terletak di sudut (dengan catatan bahwa segitiga itu adalah segitiga siku-siku atau salah satu sudut segitiga itu 90^o).

Berdasarkan segitiga pada ilustrator (di kanan), berdasarkan definisi tangen, di atas maka nilai tangen adalah

$\tan A={{\mbox{a}} \over {\mbox{b}}}\qquad \tan B={{\mbox{b}} \over {\mbox{a}}}$

Nilai tangen positif di kuadran I dan III dan negatif di kuadran II dan IV.

Hubungan tangen dengan kotangen:

$\cot A={\frac {1}{\tan A}}\,$

Hubungan nilai tangen dengan nilai sinus dan kosinusSunting

$\tan A={\frac {sinA}{cosA}}\,$

Nilai tangen sudut istimewaSunting

0°	$0$	$1$	$0$	$\infty$	$1$	$\infty$
	Sinus	Kosinus	Tangen	Kotangen	Sekan	Kosekan
8°	${\frac {\sqrt {2}}{10}}$	${\frac {7{\sqrt {2}}}{10}}$	${\frac {1}{7}}$	$7$	${\frac {5{\sqrt {2}}}{7}}$	$5{\sqrt {2}}$
15°	${\frac {{\sqrt {6}}-{\sqrt {2}}}{4}}$	${\frac {{\sqrt {6}}+{\sqrt {2}}}{4}}$	$2-{\sqrt {3}}$	$2+{\sqrt {3}}$	${\sqrt {6}}-{\sqrt {2}}$	${\sqrt {6}}+{\sqrt {2}}$
16°	${\frac {7}{25}}$	${\frac {24}{25}}$	${\frac {7}{24}}$	${\frac {24}{7}}$	${\frac {25}{24}}$	${\frac {25}{7}}$
18°	${\frac {-1+{\sqrt {5}}}{4}}$	${\frac {\sqrt {10+2{\sqrt {5}}}}{4}}$	${\frac {(-5+3{\sqrt {5}}){\sqrt {10+2{\sqrt {5}}}}}{20}}$	${\frac {(1+{\sqrt {5}}){\sqrt {10+2{\sqrt {5}}}}}{4}}$	${\frac {(5-{\sqrt {5}}){\sqrt {10+2{\sqrt {5}}}}}{10}}$	$1+{\sqrt {5}}$
30°	${\frac {1}{2}}$	${\frac {\sqrt {3}}{2}}$	${\frac {\sqrt {3}}{3}}$	${\sqrt {3}}$	${\frac {2{\sqrt {3}}}{3}}$	$2$
36°	${\frac {\sqrt {10-2{\sqrt {5}}}}{4}}$	${\frac {1+{\sqrt {5}}}{4}}$	${\frac {(-1+{\sqrt {5}}){\sqrt {10-2{\sqrt {5}}}}}{4}}$	${\frac {(5+3{\sqrt {5}}){\sqrt {10-2{\sqrt {5}}}}}{20}}$	$-1+{\sqrt {5}}$	${\frac {(5+{\sqrt {5}}){\sqrt {10-2{\sqrt {5}}}}}{10}}$
37°	${\frac {3}{5}}$	${\frac {4}{5}}$	${\frac {3}{4}}$	${\frac {4}{3}}$	${\frac {5}{4}}$	${\frac {5}{3}}$
45°	${\frac {\sqrt {2}}{2}}$	${\frac {\sqrt {2}}{2}}$	$1$	$1$	${\sqrt {2}}$	${\sqrt {2}}$
53°	${\frac {4}{5}}$	${\frac {3}{5}}$	${\frac {4}{3}}$	${\frac {3}{4}}$	${\frac {5}{3}}$	${\frac {5}{4}}$
54°	${\frac {1+{\sqrt {5}}}{4}}$	${\frac {\sqrt {10-2{\sqrt {5}}}}{4}}$	${\frac {(5+3{\sqrt {5}}){\sqrt {10-2{\sqrt {5}}}}}{20}}$	${\frac {(-1+{\sqrt {5}}){\sqrt {10-2{\sqrt {5}}}}}{4}}$	${\frac {(5+{\sqrt {5}}){\sqrt {10-2{\sqrt {5}}}}}{10}}$	$-1+{\sqrt {5}}$
60°	${\frac {\sqrt {3}}{2}}$	${\frac {1}{2}}$	${\sqrt {3}}$	${\frac {\sqrt {3}}{3}}$	$2$	${\frac {2{\sqrt {3}}}{3}}$
72°	${\frac {\sqrt {10+2{\sqrt {5}}}}{4}}$	${\frac {-1+{\sqrt {5}}}{4}}$	${\frac {(1+{\sqrt {5}}){\sqrt {10+2{\sqrt {5}}}}}{4}}$	${\frac {(-5+3{\sqrt {5}}){\sqrt {10+2{\sqrt {5}}}}}{20}}$	$1+{\sqrt {5}}$	${\frac {(5-{\sqrt {5}}){\sqrt {10+2{\sqrt {5}}}}}{10}}$
74°	${\frac {24}{25}}$	${\frac {7}{25}}$	${\frac {24}{7}}$	${\frac {7}{24}}$	${\frac {25}{7}}$	${\frac {25}{24}}$
75°	${\frac {{\sqrt {6}}+{\sqrt {2}}}{4}}$	${\frac {{\sqrt {6}}-{\sqrt {2}}}{4}}$	$2+{\sqrt {3}}$	$2-{\sqrt {3}}$	${\sqrt {6}}+{\sqrt {2}}$	${\sqrt {6}}-{\sqrt {2}}$
82°	${\frac {7{\sqrt {2}}}{10}}$	${\frac {\sqrt {2}}{10}}$	$7$	${\frac {1}{7}}$	$5{\sqrt {2}}$	${\frac {5{\sqrt {2}}}{7}}$
90°	$1$	$0$	$\infty$	$0$	$\infty$	$1$